The LessonThe greatest common factor is the largest factor that is common to two or more numbers.
Understanding the Greatest Common FactorThe numbers that multiply together to make another number are its factors. 2 is a factor of 4 because 2 × 2 = 4:
2 and 3 are factors of 6 because 2 × 3 = 6:
The greatest common factor is the largest number that is a factor for both numbers. In our example, 2 is the greatest common factor.
Another way of thinking about a factor is as a number which divides exactly into another number. 2 is the largest number that divides exactly into 4 and 6.
4 ÷ 2 = 2
6 ÷ 2 = 3
What's in a Name?The Greatest Common Factor (GCF) is so called because it is the largest (greatest) factor that is the same (common) to the numbers. It may sometimes be called:
- Greatest Common Divisor (GCD)
- Highest Common Factor (HCF)